Group table for the character group for $\textrm{Gal}(K/\mathbb{Q})$
$K$ is the global number field defined by
\( x^{8} + 6x^{6} + 36x^{4} + 216x^{2} + 1296 \)
| $\times$ | \(\chi_{ 120 } ( 1, ·)\) | \(\chi_{ 120 } ( 107, ·)\) | \(\chi_{ 120 } ( 97, ·)\) | \(\chi_{ 120 } ( 73, ·)\) | \(\chi_{ 120 } ( 11, ·)\) | \(\chi_{ 120 } ( 49, ·)\) | \(\chi_{ 120 } ( 83, ·)\) | \(\chi_{ 120 } ( 59, ·)\) |
|---|---|---|---|---|---|---|---|---|
| \(\chi_{ 120 }(1, ·)\) | \(\chi_{ 120 } ( 1, ·)\) | \(\chi_{ 120 } ( 107, ·)\) | \(\chi_{ 120 } ( 97, ·)\) | \(\chi_{ 120 } ( 73, ·)\) | \(\chi_{ 120 } ( 11, ·)\) | \(\chi_{ 120 } ( 49, ·)\) | \(\chi_{ 120 } ( 83, ·)\) | \(\chi_{ 120 } ( 59, ·)\) |
| \(\chi_{ 120 }(107, ·)\) | \(\chi_{ 120 } ( 107, ·)\) | \(\chi_{ 120 } ( 49, ·)\) | \(\chi_{ 120 } ( 59, ·)\) | \(\chi_{ 120 } ( 11, ·)\) | \(\chi_{ 120 } ( 97, ·)\) | \(\chi_{ 120 } ( 83, ·)\) | \(\chi_{ 120 } ( 1, ·)\) | \(\chi_{ 120 } ( 73, ·)\) |
| \(\chi_{ 120 }(97, ·)\) | \(\chi_{ 120 } ( 97, ·)\) | \(\chi_{ 120 } ( 59, ·)\) | \(\chi_{ 120 } ( 49, ·)\) | \(\chi_{ 120 } ( 1, ·)\) | \(\chi_{ 120 } ( 107, ·)\) | \(\chi_{ 120 } ( 73, ·)\) | \(\chi_{ 120 } ( 11, ·)\) | \(\chi_{ 120 } ( 83, ·)\) |
| \(\chi_{ 120 }(73, ·)\) | \(\chi_{ 120 } ( 73, ·)\) | \(\chi_{ 120 } ( 11, ·)\) | \(\chi_{ 120 } ( 1, ·)\) | \(\chi_{ 120 } ( 49, ·)\) | \(\chi_{ 120 } ( 83, ·)\) | \(\chi_{ 120 } ( 97, ·)\) | \(\chi_{ 120 } ( 59, ·)\) | \(\chi_{ 120 } ( 107, ·)\) |
| \(\chi_{ 120 }(11, ·)\) | \(\chi_{ 120 } ( 11, ·)\) | \(\chi_{ 120 } ( 97, ·)\) | \(\chi_{ 120 } ( 107, ·)\) | \(\chi_{ 120 } ( 83, ·)\) | \(\chi_{ 120 } ( 1, ·)\) | \(\chi_{ 120 } ( 59, ·)\) | \(\chi_{ 120 } ( 73, ·)\) | \(\chi_{ 120 } ( 49, ·)\) |
| \(\chi_{ 120 }(49, ·)\) | \(\chi_{ 120 } ( 49, ·)\) | \(\chi_{ 120 } ( 83, ·)\) | \(\chi_{ 120 } ( 73, ·)\) | \(\chi_{ 120 } ( 97, ·)\) | \(\chi_{ 120 } ( 59, ·)\) | \(\chi_{ 120 } ( 1, ·)\) | \(\chi_{ 120 } ( 107, ·)\) | \(\chi_{ 120 } ( 11, ·)\) |
| \(\chi_{ 120 }(83, ·)\) | \(\chi_{ 120 } ( 83, ·)\) | \(\chi_{ 120 } ( 1, ·)\) | \(\chi_{ 120 } ( 11, ·)\) | \(\chi_{ 120 } ( 59, ·)\) | \(\chi_{ 120 } ( 73, ·)\) | \(\chi_{ 120 } ( 107, ·)\) | \(\chi_{ 120 } ( 49, ·)\) | \(\chi_{ 120 } ( 97, ·)\) |
| \(\chi_{ 120 }(59, ·)\) | \(\chi_{ 120 } ( 59, ·)\) | \(\chi_{ 120 } ( 73, ·)\) | \(\chi_{ 120 } ( 83, ·)\) | \(\chi_{ 120 } ( 107, ·)\) | \(\chi_{ 120 } ( 49, ·)\) | \(\chi_{ 120 } ( 11, ·)\) | \(\chi_{ 120 } ( 97, ·)\) | \(\chi_{ 120 } ( 1, ·)\) |